nla review (#4321)

* simplify the nla_solver interface

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

* more simplifications

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

* init m_use_nra_model

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

* work on NSB comments

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

* work on NSB comments

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

Co-authored-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/math/lp/gomory.cpp

@@ -346,10 +346,7 @@ public:
         if (some_int_columns)
             adjust_term_and_k_for_some_ints_case_gomory();
         TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout););
-        lp_assert(lia.current_solution_is_inf_on_cut());
+        lp_assert(lia.current_solution_is_inf_on_cut());  // checks that indices are columns
-        // NSB code review: this is also used in nla_core.
-        // but it isn't consistent: when theory_lra accesses lar_solver::get_term, the term that is returned uses
-        // column indices, not terms.
         TRACE("gomory_cut", print_linear_combination_of_column_indices_only(m_t.coeffs_as_vector(), tout << "gomory cut:"); tout << " <= " << m_k << std::endl;);
         return lia_move::cut;
     }

src/math/lp/int_solver.cpp

@@ -189,7 +189,16 @@ std::ostream& int_solver::display_inf_rows(std::ostream& out) const {
     return out;
 }
 
+bool int_solver::cut_indices_are_columns() const {
+    for (const auto & p: m_t) {
+        if (p.column().index() >= lra.A_r().column_count())
+            return false;
+    }
+    return true;
+}
+
 bool int_solver::current_solution_is_inf_on_cut() const {
+    SASSERT(cut_indices_are_columns());
     const auto & x = lrac.m_r_x;
     impq v = m_t.apply(x);
     mpq sign = m_upper ? one_of_type<mpq>()  : -one_of_type<mpq>();

src/math/lp/int_solver.h

@@ -109,8 +109,8 @@ private:
     bool has_upper(unsigned j) const;
     unsigned row_of_basic_column(unsigned j) const;
     bool non_basic_columns_are_at_bounds() const;
-
+    bool cut_indices_are_columns() const;
-
+    
 public:
     std::ostream& display_column(std::ostream & out, unsigned j) const;
     constraint_index column_upper_bound_constraint(unsigned j) const;

src/math/lp/nla_basics_lemmas.cpp

@@ -220,10 +220,11 @@ void basics::negate_strict_sign(new_lemma& lemma, lpvar j) {
 // here we use the fact
 // xy = 0 -> x = 0 or y = 0
 bool basics::basic_lemma_for_mon_zero(const monic& rm, const factorization& f) {
-    // NSB review: how is the code-path calling this function disabled?
+    // it seems this code is never exercised
-    NOT_IMPLEMENTED_YET();
+    for (auto j : f) {
-    return true;
+        if (val(j).is_zero())
-#if 0
+            return false;
+    }
     TRACE("nla_solver", c().trace_print_monic_and_factorization(rm, f, tout););
     new_lemma lemma(c(), "xy = 0 -> x = 0 or y = 0");
     lemma.explain_fixed(var(rm));
@@ -235,7 +236,6 @@ bool basics::basic_lemma_for_mon_zero(const monic& rm, const factorization& f) {
     lemma &= rm;
     lemma &= f;
     return true;
-#endif
 }
 
 // use basic multiplication properties to create a lemma
@@ -285,8 +285,6 @@ bool basics::basic_lemma_for_mon_derived(const monic& rm) {
                 return true;
             if (basic_lemma_for_mon_neutral_derived(rm, factorization))
                 return true;
-            if (proportion_lemma_derived(rm, factorization))
-                return true;
         }
     }
     return false;
@@ -375,65 +373,36 @@ void basics::proportion_lemma_model_based(const monic& rm, const factorization&
         factor_index++;
     }
 }
-// x != 0 or y = 0 => |xy| >= |y|
-bool basics::proportion_lemma_derived(const monic& rm, const factorization& factorization) {
-    // NSB review: why return false?
-    return false;
-    if (c().has_real(factorization))
-        return false;
-    rational rmv = abs(var_val(rm));
-    if (rmv.is_zero()) {
-        SASSERT(c().has_zero_factor(factorization));
-        return false;
-    }
-    int factor_index = 0;
-    for (factor f : factorization) {
-        if (abs(val(f)) > rmv) {
-            generate_pl(rm, factorization, factor_index);
-            return true;
-        }
-        factor_index++;
-    }
-    return false;
-}
 
 /**
-   if there are no zero factors then |m| >= |m[factor_index]|
-
    m := f_1*...*f_n
 
-   sign_m*m < 0 or f_j = 0 or \/_{i != j} sign_j*f_j < 0 or sign_m*m >= sign_j*f_j
+   k is the index of such that |m| < |val(m[k]|
+  
+   If for all 1 <= j <= n, j != k we have f_j != 0 then |m| >= |f_k|
+
+   The lemma looks like
+   sign_m*m < 0 or \/_{i != k} f_i = 0 or sign_m*m >= sign_k*f_k
    
-NSB review:
-
-- This rule cannot be applied for reals
-  For example 1/4 = 1/2*1/2 and each factor is bigger than product.
-
-- Stronger rule is possible for integers:
-
-   sign_m*m < 0 or f_j = 0 or \/_{i != j} sign_m*m >= sign_i*f_i
-
 */
-void basics::generate_pl_on_mon(const monic& m, unsigned factor_index) {
+void basics::generate_pl_on_mon(const monic& m, unsigned k) {
     SASSERT(!c().has_real(m));
     new_lemma lemma(c(), "generate_pl_on_mon");
     unsigned mon_var = m.var();
     rational mv = val(mon_var);
+    SASSERT(abs(mv) < abs(val(m.vars()[k])));
     rational sm = rational(nla::rat_sign(mv));
     lemma |= ineq(term(sm, mon_var), llc::LT, 0);
     for (unsigned fi = 0; fi < m.size(); fi ++) {
         lpvar j = m.vars()[fi];
-        if (fi != factor_index) {
+        if (fi != k) {
             lemma |= ineq(j, llc::EQ, 0);
         } else {
-            rational jv = val(j);
+            rational sj = rational(nla::rat_sign(val(j)));
-            rational sj = rational(nla::rat_sign(jv));
-            // NSB review: what is the justification for this assert: SASSERT(sm*mv < sj*jv);
-            // NSB review: removed c().mk_ineq(sj, j, llc::LT);
             lemma |= ineq(term(sm, mon_var, -sj, j), llc::GE, 0);
         }
     }
-    lemma &= m;
+    //    lemma &= m; // no need to "explain" monomial m here
 }
 
 /**    
@@ -467,13 +436,11 @@ void basics::generate_pl(const monic& m, const factorization& fc, int factor_ind
             lpvar j = var(f);
             rational jv = val(j);
             rational sj = rational(nla::rat_sign(jv));
-            // NSB review: removed SASSERT(sm*mv < sj*jv);
-            // NSB review: removed lemma |= ineq(term(sj, j), llc::LT, 0);
             lemma |= ineq(term(sm, mon_var, -sj, j), llc::GE, 0);
         }
     }
     lemma &= fc;
-    lemma &= m;
+    lemma &= m; 
 }
 
 bool basics::is_separated_from_zero(const factorization& f) const {
@@ -539,37 +506,10 @@ void basics::basic_lemma_for_mon_model_based(const monic& rm) {
      or
      - /\_j f_j = val(f_j) => m = sign
 */
-// NSB code review: can't we just use basic_lemma_for_mon_neutral_from_factors_to_model_based?
-// then the factorization is the same as the monomial.
-// then the only difference is to omit adding some explanations.
-
 bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based_fm(const monic& m) {
-    lpvar not_one = null_lpvar;
+    lpvar not_one; rational sign;
-    rational sign(1);
+    if (!can_create_lemma_for_mon_neutral_from_factors_to_monic_model_based(m, m, not_one, sign))
-    TRACE("nla_solver_bl", tout << "m = "; c().print_monic(m, tout););
-    for (auto j : m.vars()) {
-        auto v = val(j);
-        if (v == rational(1)) {
-            continue;
-        }
-        if (v == -rational(1)) { 
-            sign = -sign;
-            continue;
-        } 
-        if (not_one == null_lpvar) {
-            not_one = j;
-            continue;
-        }
-        // if we are here then there are at least two factors with values different from one and minus one: cannot create the lemma
         return false;
-    }
-
-    if (not_one != null_lpvar) {  // we found the only not_one
-        if (var_val(m) == val(not_one) * sign) {
-            TRACE("nla_solver", tout << "the whole equal to the factor" << std::endl;);
-            return false;
-        }
-    }
        
     new_lemma lemma(c(), __FUNCTION__);
     for (auto j : m.vars()) {
@@ -621,7 +561,8 @@ bool basics::basic_lemma_for_mon_neutral_monic_to_factor_model_based(const monic
     lemma |= ineq(term(u, rational(val(u) == -val(mon_var) ? 1 : -1), mon_var), llc::NE, 0);
     lemma |= ineq(v, llc::EQ, 1);
     lemma |= ineq(v, llc::EQ, -1);
-    lemma &= rm; // NSB review: is this dependency required?
+    lemma &= rm; // NSB review: is this dependency required? - it does because it explains how monomial is equivalent
+    // to the rooted monomial
     lemma &= f;
 
     return true;
@@ -637,24 +578,11 @@ void basics::basic_lemma_for_mon_neutral_model_based(const monic& rm, const fact
         basic_lemma_for_mon_neutral_from_factors_to_monic_model_based(rm, f);
     }
 }
-
+template <typename T>
-/**
+bool basics::can_create_lemma_for_mon_neutral_from_factors_to_monic_model_based(const monic& m, const T& f, lpvar &not_one, rational& sign) {
- - m := f1*f2*.. 
+    sign = rational(1); 
-   - f_i are factors of m
+    //    TRACE("nla_solver_bl", tout << pp_mon_with_vars(_(), m) <<"\nf = " << c().pp(f) << "sign = " << sign << '\n';);
- - at most one variable among f_i evaluates to something else than -1, +1.
+    not_one = null_lpvar;
-   - m = sign * f_i
-   - sign = sign of f_1 * .. * f_{i-1} * f_{i+1} ... = +/- 1
- - lemma:
-    /\_{j != i} f_j = val(f_j) => m = sign * f_i
-    or 
-    /\ f_j = val(f_j) => m = sign if all factors evaluate to +/- 1
-
-*/ 
-bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based(const monic& m, const factorization& f) {
-    rational sign(1); 
-    SASSERT(m.rsign() == canonize_sign(f));
-    TRACE("nla_solver_bl", tout << pp_mon_with_vars(_(), m) <<"\nf = " << c().pp(f) << "sign = " << sign << '\n';);
-    lpvar not_one = null_lpvar;
     for (auto j : f) {
         TRACE("nla_solver_bl", tout << "j = "; c().print_factor_with_vars(j, tout););
         auto v = val(j);
@@ -685,6 +613,25 @@ bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based(const
         return false;        
     }
 
+    return true;
+}
+
+/**
+ - m := f1*f2*.. 
+   - f_i are factors of m
+ - at most one variable among f_i evaluates to something else than -1, +1.
+   - m = sign * f_i
+   - sign = sign of f_1 * .. * f_{i-1} * f_{i+1} ... = +/- 1
+ - lemma:
+    /\_{j != i} f_j = val(f_j) => m = sign * f_i
+    or 
+    /\ f_j = val(f_j) => m = sign if all factors evaluate to +/- 1
+
+*/ 
+bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based(const monic& m, const factorization& f) {
+    lpvar not_one; rational sign;
+    if (!can_create_lemma_for_mon_neutral_from_factors_to_monic_model_based(m, f, not_one, sign))
+        return false;
     TRACE("nla_solver_bl", tout << "not_one = " << not_one << "\n";);
         
     new_lemma lemma(c(), __FUNCTION__);

src/math/lp/nla_basics_lemmas.h

@@ -48,6 +48,10 @@ struct basics: common {
     // bool basic_lemma_for_mon_neutral_monic_to_factor_model_based_fm(const monic& m);
     bool basic_lemma_for_mon_neutral_monic_to_factor_derived(const monic& rm, const factorization& f);
 
+    // use the fact
+    // 1 * 1 ... * 1 * x * 1 ... * 1 = x
+    template <typename T>
+    bool can_create_lemma_for_mon_neutral_from_factors_to_monic_model_based(const monic& rm, const T&, lpvar&, rational&);
     // use the fact
     // 1 * 1 ... * 1 * x * 1 ... * 1 = x
     bool basic_lemma_for_mon_neutral_from_factors_to_monic_model_based(const monic& rm, const factorization& f);
@@ -83,8 +87,6 @@ struct basics: common {
     void negate_strict_sign(new_lemma& lemma, lpvar j);
     // x != 0 or y = 0 => |xy| >= |y|
     void proportion_lemma_model_based(const monic& rm, const factorization& factorization);
-    // x != 0 or y = 0 => |xy| >= |y|
-    bool proportion_lemma_derived(const monic& rm, const factorization& factorization);
     // if there are no zero factors then |m| >= |m[factor_index]|
     void generate_pl_on_mon(const monic& m, unsigned factor_index);
     

src/math/lp/nla_common.h

@@ -49,6 +49,9 @@ struct common {
     rational var_val(monic const& m) const; // value obtained from variable representing monomial
     rational mul_val(monic const& m) const; // value obtained from multiplying variables of monomial
     template <typename T> lpvar var(T const& t) const;
+    // this needed in can_create_lemma_for_mon_neutral_from_factors_to_monic_model_based when iterating
+    // over a monic
+    lpvar var(lpvar j) const { return j; }
     bool done() const;
     template <typename T> bool canonize_sign(const T&) const;
 

src/math/lp/nla_core.cpp

@@ -1476,21 +1476,16 @@ lbool core::check(vector<lemma>& l_vec) {
     patch_monomials_with_real_vars();
     if (m_to_refine.is_empty()) { return l_true; }   
     init_search();
-
+  
     set_use_nra_model(false);    
-    
-    if (need_to_call_algebraic_methods() && m_horner.horner_lemmas())
-        goto finish_up;
 
-
+    if (need_to_call_algebraic_methods()) {
-    if (!done()) {
+        if (!m_horner.horner_lemmas() && m_nla_settings.run_grobner() && !done()) {
-        clear_and_resize_active_var_set();  // NSB code review: why is this independent of whether Grobner is run?
+            clear_and_resize_active_var_set(); 
-        if (m_nla_settings.run_grobner()) {
             find_nl_cluster();
-            run_grobner();
+            run_grobner();                
         }
     }
-
     TRACE("nla_solver_details", print_terms(tout); tout << m_lar_solver.constraints(););
     if (!done()) 
         m_basics.basic_lemma(true);    
@@ -1511,6 +1506,7 @@ lbool core::check(vector<lemma>& l_vec) {
             m_tangents.tangent_lemma();
     }
 
+
     if (!m_reslim.inc())
         return l_undef;
   

src/math/lp/nla_core.h

@@ -404,7 +404,6 @@ public:
     bool rm_check(const monic&) const;
     std::unordered_map<unsigned, unsigned_vector> get_rm_by_arity();
 
-    // NSB code review: these could be methods on new_lemma
     void add_abs_bound(new_lemma& lemma, lpvar v, llc cmp);
     void add_abs_bound(new_lemma& lemma, lpvar v, llc cmp, rational const& bound);
     void negate_relation(new_lemma& lemma, unsigned j, const rational& a);

src/math/lp/nla_solver.cpp

@@ -28,7 +28,6 @@ bool solver::is_monic_var(lpvar v) const {
 
 bool solver::need_check() { return true; }
 
-
 lbool solver::check(vector<lemma>& l) {
     return m_core->check(l);
 }

src/smt/theory_lra.cpp

@@ -2158,6 +2158,7 @@ public:
     }
     
     lbool check_nla_continue() {
+        m_a1 = nullptr; m_a2 = nullptr;
         lbool r = m_nla->check(m_nla_lemma_vector);
         if (use_nra_model()) m_stats.m_nra_calls ++;